2.8 Saturation

Saturation is another way to reduce the size of an integer value. Saturation is useful when you want to convert a larger object to a smaller object and you're willing to live with possible loss of precision. If the value of the larger object is not outside the range of the smaller object, you can convert the value via saturation by copying the LO bits of the larger value into the smaller object. If the larger value is outside the smaller object's range, then you clip the larger value by setting it to the largest (or smallest) value within the range of the smaller data type.

When converting a 16-bit signed integer to an 8-bit signed integer, if the 16-bit value is in the range ˆ’ 128..+127 you simply copy the LO byte into the 8-bit object. If the 16-bit signed value is greater than +127, then you clip the value to +127 and store +127 into the 8-bit object. Likewise, if the value is less than ˆ’ 128, you clip the final 8-bit object to ˆ’ 128. Saturation works the same way when clipping 32-bit values to smaller values. If the larger value is outside the range of the smaller value, then you simply clip the value to the closest value that you can represent with the smaller data type.

If the larger value is outside the range of the smaller value, there will be a loss of precision during the conversion. While clipping the value is never desirable, sometimes this is better than raising an exception or otherwise rejecting the calculation. For many applications, such as audio or video, the clipped result is still recognizable to the end user , so this is a reasonable conversion scheme in such situations.

As a result, many CPUs support saturation arithmetic in their special 'multimedia extension' instruction sets. On the Intel 80x86 processor family, for example, the MMX instruction extensions provide saturation capabilities. Most CPUs' standard instruction sets, as well as most high-level languages, do not provide direct support for saturation, but saturation is not difficult. Consider the following Pascal/Delphi/Kylix code that uses saturation to convert a 32-bit integer to a 16-bit integer:

 var     li :longint;     si :smallint;        . . .     if( li > 32767 ) then             si := 32767;             else if( li < -32768 ) then             si := -32768;             else         si := li;